1. **Problem:** Evaluate $\frac{6}{11} \div \left(-\frac{3}{5}\right)$. 2. **Formula and rule:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ 3. **Apply the formula:** $$\frac{6}{11} \div \left(-\frac{3}{5}\right) = \frac{6}{11} \times \left(-\frac{5}{3}\right)$$ 4. **Multiply numerators and denominators:** $$= \frac{6 \times (-5)}{11 \times 3} = \frac{-30}{33}$$ 5. **Simplify the fraction:** Both numerator and denominator can be divided by 3: $$= \frac{\cancel{3} \times (-10)}{\cancel{3} \times 11} = \frac{-10}{11}$$ 6. **Final answer:** $$\boxed{-\frac{10}{11}}$$ **Answer choice:** A. $-\frac{10}{11}$